Pour water into a large bowl and sprinkle yeast over top. Let stand for a few minutes to dissolve. Mix in oil, salt, and flour to make a dough. When dough is too stiff to stir, turn out onto a floured surface, and knead for about 5 minutes. Place into an oiled bowl, and cover with a clean towel. Set aside to rise for about 45 minutes.
Place figs into a small bowl, and pour boiling water over them. Let stand for about 10 minutes, then drain and chop. Set aside.
Meanwhile, heat 1 tablespoon of olive oil in a skillet over medium heat. Add onions; cook and stir until they are wilted and soft. Reduce heat to low, and season with salt. Continue to cook and stir until onions are dark brown, 5 to 10 minutes. Stir in thyme, fennel seed, and figs, and remove from the heat.
Preheat the oven to 450 degrees F (220 degrees C). Punch down pizza dough, and stretch into a circle about 1/4-inch thick. Place on a lightly greased pizza pan or baking sheet. Brush surface lightly with remaining olive oil. Spread onion and fig mixture over crust. It will be sparse, but there is plenty of flavor. Dot with pieces of goat cheese.
Bake for 15 to 18 minutes in the preheated oven, or until crust has turned golden brown at edges.